Finite Group Databasebeta

C23×D4×D8 #72304231

order1024
nilpotency class3
automorphism?
homologyAbelianization (H1) = C27 · Schur multiplier (H2) = C221

Aliases

direct productC23×D4×D8

Subgroups

subgroupG/H
center, socleC25C22×D4
commutator, Frattini, cosocleC2×C4C27
LCSG ▷ C2×C4 ▷ C2 ▷ C1
UCSC1 ◁ C25 ◁ C23×C4×D4 ◁ G
LECSG ▷ C2×C4 ▷ C2 ▷ C1

158645 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 256

Conjugacy classes & character table

280 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup ofC23×D4×AGL(1,ℤ/8), C23×#61451, C22×#6574130, …
maximal normal subgroup ofC23×D4×AGL(1,ℤ/8), C23×#61451, C22×#6574130, …
maximal quotient ofC22×D8×#120, C22×#6576538, C22×D4×#509, …

GAP

Past the SmallGroups library coverage — no SmallGroups id.